4) A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is walking away from the pole at a rate of 2 ft/sec. a. At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? b. At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole?

A) 48/13 ft/sec

B) 22/13 ft/sec

Step-by-step explanation: Given that:

A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.

A) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?

Using similar triangles, we can say:

12/L = 55/(L - x)

Cross multiply to get:

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Taking the derivative with respect to time we get:

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

Since dx/dt = 2 so

dl/dt = (12/6.5)(2)

= 24/6.5

= 48/13 ft/sec

B) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole ?

Subtract the rate the shadow is going from the rate the man is going. Therefore

48/13 - 2 = 22/13 ft/sec.